"Has" or "Have" with "Each"?

This is from a multiple choice question with 4 options, but I narrowed it down to 2:

Select the best version of the following sentence: (there is really no sentence after this, just the answer choices)

• a) Each of the conference rooms has a computer display.

• d) Each of the conference rooms have computer displays.

In my eyes these choices are both perfectly fine, I can't see anything wrong with either of them.

Solution 1:

TL;DR: The rule is each is always singular (apart from contrived contexts). But lots of learners and even some native speakers can be thrown by each of the [plural noun], and treat it as plural.

From grammar.ccc.commnet...

Each is often followed by a prepositional phrase ending in a plural word (Each of the cars), thus confusing the verb choice. [italics mine]

I expect most people would simply take it for granted that each is always singular, regardless of whether it happens to be just one word in the construction each of the [plural noun], but this NGram is interesting (it suggests the usage was much more common a couple of centuries ago).

And let's not forget indisputably valid usages such as We each of us have our faults. It takes some doing to figure out exactly why the presence of the apparently optional we there precludes us from continuing with the equally valid (as a complete sentence) Each of us has his faults (I'm guessing it's because the actual subject is plural we and that each is an adjective in an adjectival modifier, but what do I know?).